In this letter we investigate the rupture instability of thin liquid films by means of a bifurcation analysis in the vicinity of the short-scale instability threshold. The rupture time estimate obtained in closed form as a function of the relevant dimensionless groups is in striking agreement with the results of the numerical simulations of the original nonlinear evolution equations. This sugge...

The present work investigates the parametric instability of parallel propagating circularly polarized Alfvén pump waves in a collisional dusty plasma. It is demonstrated that the relative drift between the charged dust and the electrons and ions gives rise to the Hall effect resulting in the modified pump wave characteristics. Although the linearized fluid equations with periodic coefficients a...

The evolution of modulational instability, or Benjamin-Feir instability is investigated within the framework of the two-dimensional fully nonlinear potential equations, modified to include wind forcing and viscous dissipation. The wind model corresponds to the Miles’ theory. The introduction of dissipation in the equations is briefly discussed. Evolution of this instability in the presence of d...

In this paper, we study the stability and evolution of solitary waves in perturbed generalized nonlinear Schrödinger (NLS) equations. Our method is based on the completeness of the bounded eigenstates of the associated linear operator in L2 space and a standard multiple-scale perturbation technique. Unlike the adiabatic perturbation method, our method details all instability mechanisms caused b...

We report a detailed experimental study of vector modulation instability in highly birefringent optical fibers in the anomalous-dispersion regime. We prove that the observed instability is mainly induced by vacuum fluctuations. The detuning of the spectral peaks agrees with linear perturbation analysis. The exact shape of the spectrum is well reproduced by numerical integration of stochastic no...

We propose an efficient method for computing coupled flow–body dynamics. The time-stepping is implicit, and uses an iterative method (preconditioned GMRES) to solve the flow–body equations. The preconditioner solves a decoupled version of the equations which involves only the inversion of banded matrices, and requires a small number of iterations per time step. We use the method to probe the in...

Received ; accepted – 2 – ABSTRACT The present work investigates the parametric instability of parallel propagating circularly polarized Alfvén (pump) waves in a weakly ionized molecular cloud. It is shown that the relative drift between the plasma particles gives rise to the Hall effect resulting in the modified pump wave characteristics. Although the linearized fluid equations with periodic c...

Stability analysis of the numerical Method of characteristics applied to energy-preserving systems. Abstract We study numerical (in)stability of the Method of characteristics (MoC) applied to a system of non-dissipative hyperbolic partial differential equations (PDEs) with periodic boundary conditions. We consider three different solvers along the characteristics: simple Euler (SE), modified Eu...

Slender asymptotic ber models are derived from Doi-type 3{D equations for free surface ows of liquid crystalline polymers. Leading order equations and self{consistent corrections are presented for a variety of physical regimes. We then explore the coupling of orientation e ects to slender elongational ow behavior, with particular focus on the interplay between the Rayleigh capillary instability...